The study of deriving a higher order moving mesh scheme -

Abstract

The formulation and implementation of a higher-order accurate scheme for arbitrary moving mesh problems, is presented. The governing equations are formulated according to the Arbitrary Lagrangian-Eulerian (ALE) approach in a form that satisfies the Geometrical Conservation Laws (GCL) in an intrinsic manner. The contribution of this work is achieved by the technique used to deal with the introduced moving mesh term represented by face mesh velocities. The method replaces the aforementioned face mesh velocities by equivalent volumetric face increments on which the formulated explicit higher order scheme is applied. The scheme is implemented on the three dimensional MATLAB unstructured Finite Volume Method (u-FVM) solver where several test cases are conducted and simulated on static and arbitrary moving grids with their results being presented and analyzed. The results indicate that the set obtained from higher order mesh treatment tend to overlap with the results of the static mesh, hence, proving the effectiveness of the formulated scheme.